This is an interview question that causes more consternation than just about any other. Here are some suggestions that will help you give an outstanding answer:
1) Like all other aspects of a job search, tailor your response to the specific job you're seeking.
Just like you shouldn't have a "one-size-fits-all" resume, you shouldn't have a "one-size-fits all" weakness. If you're interviewing for a job that's heavily dependent on teamwork you probably don't want to specify something like "I wish I were more comfortable asking for help." If it's a data-heavy job, "I sometimes rely too much on my gut" would be an inappropriate characteristic. And if the job involves supervising a number of people "difficulty in delegating" might not be the best choice to mention. Ideally you should select a weakness whose antidote process speaks directly to the kind of strength that will be particularly valued by the employer. For example, if the job requires the processing of a large number of requests from multiple stakeholders you might mention "a difficulty with time management" while noting that the time management challenge has taught you a lot about setting priorities and establishing realistic deadlines.
2) Focus on a physical, rather than a personality or style, characteristic.
You might say "because I'm young-looking some people don't take me as seriously as I deserve to be taken;" or "because I'm older some younger employees start off thinking that my ideas are dated;" or "because I have a somewhat high-pitched voice men tend to think I'm inexperienced." The advantage of citing a physical characteristic and then describing steps you've taken to address it (e.g. if young-appearing "I dress a little more formally than I otherwise might," if older "I pay particular attention to my dress and speech being contemporary") shows you are able to make the most of the cards you're dealt. That's a quality all employers are going to value.
3) Cite a trait that is clearly able to be improved upon, vs. one that is more intractable.
"I'm not as comfortable with technology as I'd like to be"" is obviously a weakness, but it's also one that is easy to improve upon (e.g. "I've hired a tutor to teach me html; I've enrolled in a social media certification program"). Same with "I tend to get nervous when I need to speak in front of a group" (solution: "I've enrolled in Toastmasters and have already seen a difference in my confidence level). Contrast those weaknesses with ones related more to your basic personality, such as "I tend to be very impatient" or "I dislike confrontation" - weaknesses that would be a lot harder to convincingly improve upon.
A couple of additional points:
- Make sure you have an anecdote that illustrates your weakness and the improvement that you claim to have made.
- Avoid the temptation to cite a weakness that is actually a strength in disguise. "I'm a perfectionist" can be easily flipped to the strength of turning out superior work, and "I sometimes sacrifice my personal life for my job" suggests exceptional dedication to the employer," but they're clichéd responses that most interviewers will see right through.
Remember that the employer is probably looking less at which particular weakness you cite and more at your self-awareness and the process you've undertaken to address the weakness.